Determination of mechanical design properties of elastic materials

ABSTRACT

Mechanical design properties of elastic materials including design stress and design modules are determined from the energy dissipation per cycle and total elastic energy of a sample used as a spring in a one degree of freedom oscillator whose fixed end is subjected to a transient displacement during each cycle. The energy dissipation per cycle and total elastic energy are related to the steady state amplitude and frequency, respectively, of the oscillator.

United States Patent [191 Weissmann Jan. 22, 1974 DETERMINATION OFMECHANICAL DESIGN PROPERTIES OF ELASTIC MATERIALS [75] Inventor: GerdFriedrich Horst Weissmann,

Florham Park, NJ.

[73] Assignee: Bell Telephone Laboratories,

Incorporated, Murray Hill, NJ.

[22] Filed: Mar. 15, 1972 [21] Appl. No.: 234,781

[52] US. Cl. 73/67.2, 73/100 [51] Int. Cl. G0lm 7/00, GOln 3/38 [58]Field of Search 73/67.1, 67.2, 67.3, 67.4,

[56] References Cited UNITED STATES PATENTS 2,283,453 5/1942 Norton73/67.1

3,319,460 5/1967 Barigant 73/67.2 3,417,608 12/1968 Barigant 73/67.l3,610,027 10/1971 Woboditsch 13/672 Primary Examiner-Charles A. RuehlAttorney, Agent, or Firm-John C. Fox

[5 7] ABSTRACT Mechanical design properties of elastic materialsincluding design stress and design modulus are determined frdm theenergy dissipation per cycle and total elastic energy of a sample usedas a spring in a one degree of freedom oscillator whose fixed end issubjected to a transient displacement during each cycle.

.The energy dissipation per cycle and total elastic energy are relatedto the steady state amplitude and frequency, respectively, of theoscillator.

7 Claims, 4 Drawing Figures PATENTEDJAN 22 1914 SHEET l 0? 2 IllllPATENTEnJmz r014 DESIGN STRESS 0-, (MN/ SHEET 2 [If 2 REDUCTION 'gegg,/COPPER l50- o ,QBERYLLIUM i EICUPRONICKEL IHNPHOSPHOR BRONZE |0o--I|\ALUM|NUM MODULUS 0F ELASTICITY 1 FROM TENSION TEST COPPER dd FIG 4BERYLLIUM GKJPHOSPHOR BRONZE STAlN LESS STEEL CUPRONICKEL (95%)CUPRONICKEL (60%) CUPRONICKEL (37%) CUPRONICKEL (0%) l i 500 I000 0.01%OFFSET YIELD STRESS 6 (MN 2) DETERMINATION OF MECHANICAL DESIGNPROPERTIES OF ELASTIC MATERIALS BACKGROUND OF THE INVENTION Thisinvention relates to an apparatus and method for determining mechanicaldesign properties of elastic materials by measuring the energydissipation per cycle and elastic energy of a sample in steady statecyclic bending or torsion of constant amplitude.

Most mechanical and structural parts are designed to operate in theelastic range of the materials used whether such parts be heavy girdersof highway bridges or simple mechanical springs for use incommunications equipment. For an adequate analysis of these parts, themodulus of elasticity and a design stress of the materials must beavailable. These values are traditionally determined by means of tensiontests in which a stress-strain curve for the material is usuallyobtained. The slope of the curve in the elastic range of the material isdesignated as the elastic modulus. The intersection'of a line parallelto this slope with the stress-strain curve then determinesthe offsetyield stress for a specified offset, which is used as the permissiblestress. Due to factors such as experimental error. and materialcharacteristics, the stress-strain relationship may often deviatesomewhat from linearity, requiring a degree of subjectivity andconsequently a significant probability of error in the determination ofthe elastic modulus and accordingly,'the yield stress. Furthermore, the0.01 percent yield stress, although generally considered to indicate theonset of permanent deformation and to be a reasonable approximation ofthe proportional limit, nevertheless is generally not reported bymaterial suppliers since -a small error in the determination of theelastic modulus often leads to a large error in the determination of the0.01 percent yield stress by the above method. Additional complicatingfactors include, for example, the following:( 1 for some high strengthmaterials the 0.0l percent yield stress represents reversible changes inthe geometry of the specimen rather than the onset of permanentdeformation, (2) due to the Bauschinger effect certain strain-hardenedmaterials may exhibit lower 0.01 percent yield stresses in compressionthan in tension, and (3) repeated stressing may cause cyclic hardeningor softening of some materials, resulting in variations in designproperties depending upon the mechanical history of the sample.

Due in part to the recognition of the limitations of tension testing forthe determination of the elastic modulus of materials, various dynamictesting methods have been explored. For example, frequency measurementsof both free vibrations and forced harmonic vibrations of a sample havebeen used to obtain values for the elastic modulus. At present, thereexists no suitable alternative for tension tests for the determinationof permissible design stresses such as the .01 percent yield stress.

SUMMARY OF THE INVENTION Mechanical design properties of elasticmaterials including design modulus and design stress may readily bedeterminedv by measuring the elastic energy and the energy dissipationper cycle, respectively, of a strip or wire sample in cyclic bending ortorsion as the spring in a one degree of freedom oscillator whose freeend has a weighted part attached andwhose fixed end is subjected to atleast one transient displacement during each bend or torsion cycle. Suchan arrangement results in the achievement of a steady state oscillationof constant amplitude. The design modulus is then a function of thetotal elastic energy of the sample which is a function of the frequencyof rotation according to the following relationship:

wherein Z is the design modulus,

l is the sample length,

b is the sample width,

h is the sample thickness,

J is the mass moment of inertia of the attachment part, and

f is the frequency of rotation of the part.

In a preferred embodiment the mass moment of inertia of the attachmentpart is chosen so as to achieve a low to moderate frequency of rotation(e.g., 0.5 to 200 Hertz) so as to minimize energy losses due to airfriction and to avoid the dependence of energy dissipation per cycleupon the strain rate which would occur for some materials at higherfrequencies of rotation.

The magnitude of the transient displacement determines the energy inputinto the system per cycle which under a steady state condition equalsthe energy dissipation per cycle. For stresses above the onset ofpermanent deformation, the energy dissipation per cycle is anexponential function of the total strain or total stress, which isdetermined by the amplitude of the angle of rotation of the attachmentpart.

The magnitude of the transient displacement determines the maximumpermanent strain or offset for the design stress, and for the case ofbending is determined according to the following relationship:

where 0,, is the transient displacement,

l is the length of the sample,

h is the thickness of the sample, and

A: is the design offset.

The design stress is then a function of the maximum amplitude achievedfor a steady state condition according to the following relationship:

where 0', is the design stress, E is the design modulus, As is theoffset, and e, is the design strain which is a function of the steadystate amplitude of the angle of rotation according to the relationship:

where 4),, is the steady state or maximum amplitude.

Other design properties which may be determined from the frequencyand/or amplitude values include bending stiffness per unit width,permissible bending moment per unit width, and the maximum modulus.

As used herein, the term elastic material is meant to refer to anymaterial which exhibits at least some elastic behavior under thespecified test conditions.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a perspective view of themechanical parts of one embodiment of an apparatus suitable for carryingout bend tests in accordance with the invention;

FIG. 2 is a schematic diagram depicting the operation of the apparatusof FIG. 1 as viewed along the axis of rotation of the apparatus;

FIG. 3 is a graph comparing the modulus of elasticity as determined fromtension tests with the modulus of elasticity as determined from the bendtest of the invention for several metal alloy materials; and

FIG. 4 is a graph comparing the 0.01 percent offset yield stress asdetermined by tension tests with the design stress for a 0.01 percentoffset as determined by the bend test of the invention for various metalalloy materials.

DETAILED DESCRIPTION OF THE INVENTION Referring now to FIG. 1, there isshown one embodiment of an apparatus for the evaluation of metal stripssubjected to substantially uniform bending. Base plate is rotatablymounted upon supports [la and 11b by means of blocks 12a and 12battached to the base plate and supported by bearings 13a and 13b.Clamping support 14 on base plate 10 supports sample strip 15 in a restposition while attachment part 16 is attached to the upper free end ofstrip [5 by means of clamp 16c. Bars 16a and 16b of attachment part 16extend through slot shaped apertures which are formed by base plate 10.It is preferred to choose sample dimensions such that the length l is atleast l2 times the thickness h in order to reduce the effect of energylosses in the clamps. A spacer may be used when clamping attachment part16 to the upper end of the sample in order to insure a uniform lengthfrom sample to sample. The length, therefore, is the exposed length anddoes not include those portions of the sample between the clamps.

The mass moment of inertia of the attachment part [6 may be eithercalculated or determined experimentally by well known techniques.

In general, where samples of different thicknesses are to be tested inthe same apparatus, it is preferred to have different attachment partsfor different standard thicknesses so as to achieve the desired lowfrequency of the bending. In addition, for some materials, such ascertain viscoelastic materials, design properties may be strain ratedependent. In such cases such dependence may be determined bydetermining the design properties at various frequencies using thedifferent attachment parts. In addition, it has been found advantageousto achieve a relatively large mass moment of inertia for a relativelylow weight of the attachment part since such results in low normalstresses compared to bending stresses.

The purpose of blocks 12a and 12b is to enable positioning of the sampleso that its center lies upon the axis of rotation R of the base plate inorder to reduce the effect of gravity and nonlinearities of theapparatus for angles of rotation of the sample up to 30 to aninsignificant amount. The axis of rotation is thus displaced from butparallel to the center line 4) of the base plate.

Referring now to FIG. 2, there is shown schematically the operation ofthe apparatus of FIG. 1. Base plate 10 is held in a fixed position y, bysolenoid 18. Once the sample has been clamped onto base plate 10 andpart 16 has been attached to the free end of the sample, attachment part16 is then set in motion by moving bars 16a and 16b from the restposition shown in the Figure past optical switch 19 causing theactuation of solenoid l7 and the rotation of base plate 10 to position yby an amount equivalent to 6 Part 16 then returns of its own momentum,passing optical switch l9 again in the opposite direction, but resultingin no change in the position of base plate 10 until the part passesoptical switch 20 causing the actuation of solenoid l8 and the rotationof base plate 10 back to position y, by an amount equal to 6 When bars16a and 16b pass optical switch 20 again in the opposite direction, nochange occurs in the position of base plate 10 until optical switch l9isagain actuated. A simple logic circuit controls the interaction betweenthe optical switches and the solenoids. After a few cycles, typicallyabout 10, the angle of rotation of the attachment part reaches a maximumvalue of 4) indicating that a steady state condition has been reached.The positions of the optical switches are adjustable. The positions ofthe solenoids are also adjustable so that the angle of rotation 0,, ofbase plate 10 is also adjustable. As stated above, the angle 0,, isdetermined by the offset desired for the design stress according toequation (2) above.

bending moment per unit width,

M, 0.0175 C (42,, 6 and maximum modulus,

EXAMPLE Using apparatus similar to that depicted in FIGS. 1 and 2,design properties of several alloys were determined. Table I shows thealloys and their temper, the sample dimensions b, h, and l, the measuredangles of rotation of the samples da the measured frequency f, thedesign strain e., the design modulus E, determined by the bend test, thedesign stress a, for an irreversible strain of A6 0.0001 determined bythe bend test, and the elastic modulus E determined by conventionaltension testing and the 0.01 percent yield stress 0 determined byconventional tension testing, all values reported both in metric and U.S. customary units.

A single attachment part was used having the mass moment of inertiashown at the top of Table 1.

Section 1 MATERIAL l h b mm mm mm (in.) (l'in) (in.) Cupro nickel CA7253.162 0.156 12.7 95% Reduction (0.1245) (6.15) (0.5) Cupro-nickel CA-7253.162 0.157 12.7 60% Reduction (0.1245) (6.20) (0.5) Cupro-nickel CA-7253.162 0.151 12.7 37% Reduction (0.1245) (5.95) (0.5) Cupro-nickel CA-7253.162 0.161 12.7 0% Reduction (0.1245) (6.35) (0.5) Stainless Steel 3013.162 0.131 14.29

Copper Beryllium CA-l72 3.162 0.267 11.99 96.5% Reduction (0.1245)(10.50) (0.4722) Aluminum 1100 H14 6.363 0.300 12.31 (0.2505) (11.80)(0.485) Phosphor Bronze CA-5l0 3.162 0.263 12.22

Section 2 MATERIAL 4),, f

deg. Hz Cupro-nickel CA-725 11.0 1.41 4.12 95% Reduction Cupro-nickelCA-7Z5 9.0 1.45 3.39 60% Reduction Cupro-nickel CA-725 11.5 1.36 3.0837% Reduction Cupro-nickel CA-725 3.0 1.49 0.88 0% Reduction StainlessSteel 301 12.0 1.27 3.77 Copper Beryllium CA-172 15.0 3.23 9.43 96.5%Reduction Aluminum 1100 H14 3.5 1.11111 1.25 Phosphor Bronze CA-510 10.5I 2.80 6.63

Section 3 MATERIAL E a GN/m MN/m GN/m MN/m (10ksi) (ksi) l0' ksi) (ksi)Cupro-nickcl CA-725 133 534 129 465 95% Reduction (19.2) (77.1) (18.7)(67.4) Cupro-nickel CA-725 138 463 I35 439 60% Reduction (19.8) (65.3)(19.6) (63.6) Cupro-nickel CA-725 136 406 138 400 37% Reduction (19.7)(58.7) (20.0) (58.0) Cupro-nickel CA-725 135 143 126 131 0% Reduction(19.4) 20.6) (18.3) (19.0) Stainless Steel 301 162 594 -552" (23.5)(86.3) (-80.0) Copper Beryllium CA-l72 147 1400 148 1180 96.5% Reduction(21.4) (203.2) (21.5) (171.0) Aluminum 110() H14 64 74 69 (9.4) (10.8)(10.0) Phosphor Bronze (IA-510 114 741 116 717 (16.5) (10.7) (16.11)(10.4)

40% of Tensile Strength FIG. 3 is a graph comparing the elastic modulidetermined by means of the bend tests of the invention and tensiontests. As may be seen, there is good agreement between these methods. Inaddition, for the comenickel alloys the bend tests yielded a smallervariation in values than did the tensile tests as may be verified fromthevalues reported in Table 1.

FIG. 4 shows a comparison of the design stress determined by the bendtest of the invention and the 0.01 percent offset yield stressdetermined by tensile tests. As may be seen, for metals with tempersindicating relatively small amounts of cold work, there is goodagreement between the values of both methods, indicating that deviationsfrom linearity measured by the tensile tests were caused by permanentdeformation of the sample. For the .cupro-nickel alloy and theberylliumcopper alloy having a percent cold reduction, the bend testmeasured higher stress values than did the tension test, indicating thatthe deviation from linearity observed in the tension tests was in partreversible and that the beginning of permanent deformation takes placeat higher stress levels.

The results shown in Table l and FIGS. 3 and 4 were obtained for lessthan 200 cycles of operation of the bend test. The 95 percent reducedcupro-nickel alloy was subjected in a separate bend test to 2,500 cyclesresulting in a significant reduction in the design stress from 534 MN/m(77.1 ksi) to 469 MN/m (68.1 ksi) indicating cyclic softening.

The invention has been described in terms of a limited number ofpreferred embodiments. However, it is to be understood that otherembodiments which rely upon the principles set forth herein are part ofthe invention. For example, measurement of elastic energy and the energydissipation per cycle of a wire or rod sample in bending or torsion inorder to derive values of design properties for such samples iscontemplated. Furthermore, the orientation of the sample may behorizontal, rather than vertical. For example, the bend axis of a stripcould be normal to a horizontal plane.

What is claimed is:

1. An apparatus for determining the mechanical design properties ofelastic materials comprising:

means for supporting a sample, the means holding the sample at one endthereof,

a weighted part attached to the other end of the sample, and

means for producing a periodic transient displacement of the supportingmeans of a variable magnitude so as to induce periodic motion of thesample, and

means for actuating the displacement means in response to the samplemotion, the actuating means comprising the weighted part attached to theother end of the sample and switching means responsive to the motion ofthe weighted part operatively connected to the displacement means, so asto achieve a steady state oscillation of the sample.

2. The apparatus of claim 1 in which the sample is a strip having alength l at least 12 times its thickness h and in which the oscillationcomprises a uniform cyclic bending of the strip about a bend axistransverse to the length of the strip.

3. The apparatus of claim 2 in which:

the sample strip supporting means comprises at least two supportingmembers, a base plate, two blocks mounted near opposite edges of thebase plate and on a center line through the center of gravity of thebase plate, the blocks rotatably mounted on the supporting members so asto achieve rotation of the base plate about an axis of rotationdisplaced from but parallel to the center line of the base plate, thebase plate defining two parallel slot shaped apertures, the longdimensions of the apertures being normal to the axis of rotation of thebase plate, and a first holder mounted on the base plate between theapertures and on the center line of the base plate;

the weighted part comprises a second holder and two elongated members ofsubstantially equal weight and dimensions attached to opposite ends ofthe holder and extending through the apertures, the

center of gravity of the weighted part being approximately on thedisplaced axis of rotation of the base plate, and

the displacement means comprises at least one solenoid movably mountednear one end of the base plate, so that actuating the solenoid producesan attractive force upon the base plate and causes a resultant rotationof the base plate toward the solenoid.

4. The apparatus of claim 3 in which the means for actuating thesolenoid comprises at least one optical switch movably mounted withinthe path of rotation of the attachment part and circuit means forcontrolling the interaction between the optical switch and the solenoidso that traversal of the optical switch by the weighted part results inthe alternate actuation and deactuation of the solenoid.

5. A method for determining the mechanical design properties of elasticmaterials comprising:

supporting a sample at one end,

attaching a weighted part to the other end of the sample,

producing a periodic transient displacement of the supported end of thesample so as to induce periodic motion of the sample, the magnitude ofthe displacement being of a predetermined value, and the period of thedisplacement being determined by the period of the sample, so as toachieve a steady state oscillation of the sample.

6. The method of claim 5 in which the transient displacement produced isangular, and its magnitude is determined by the relationship:

where l is the length of the sample, h is the thickness of the sample,and

A6 is the desired maximum permanent deformation,

and in which the design modulus is related to the steady state frequencyof oscillation of the sample E 473.7 lJ/bh j wherein E is the designmodulus,

l is the sample length,

b is the sample width,

h is the sample thickness,

J is the mass moment of inertia of the attachment part, and

fis the measured frequency of rotation of the part,

and the design stress is related to the steady state amplitude ofoscillation of the sample according to:

0 E (e, As)

where is the design stress,

E is the design modulus,

A6 is the offset, and

e, is the design strain which is a function of the steady stateamplitude of the angle of rotation according to the relationship:

e 0.00759 (h/l) (1),,

where d) is the steady state or maximum amplitude. 7. The method ofclaim 5 in which the sample is a strip having a length at least 12 timesits thickness h and in which the oscillation comprises a uniform cyclicbending of the strip about a bend axis transverse to the length of thestrip.

1. An apparatus for determining the mechanical design properties ofelastic materials comprising: means for supporting a sample, the meansholding the sample at one end thereof, a weighted part attached to theother end of the sample, and means for producing a periodic transientdisplacement of the supporting means of a variable magnitude so as toinduce periodic motion of the sample, and means for actuating thedisplacement means in response to the sample motion, the actuating meanscomprising the weighted part attached to the other end of the sample andswitching means responSive to the motion of the weighted partoperatively connected to the displacement means, so as to achieve asteady state oscillation of the sample.
 2. The apparatus of claim 1 inwhich the sample is a strip having a length l at least 12 times itsthickness h and in which the oscillation comprises a uniform cyclicbending of the strip about a bend axis transverse to the length of thestrip.
 3. The apparatus of claim 2 in which: the sample strip supportingmeans comprises at least two supporting members, a base plate, twoblocks mounted near opposite edges of the base plate and on a centerline through the center of gravity of the base plate, the blocksrotatably mounted on the supporting members so as to achieve rotation ofthe base plate about an axis of rotation displaced from but parallel tothe center line of the base plate, the base plate defining two parallelslot shaped apertures, the long dimensions of the apertures being normalto the axis of rotation of the base plate, and a first holder mounted onthe base plate between the apertures and on the center line of the baseplate; the weighted part comprises a second holder and two elongatedmembers of substantially equal weight and dimensions attached toopposite ends of the holder and extending through the apertures, thecenter of gravity of the weighted part being approximately on thedisplaced axis of rotation of the base plate, and the displacement meanscomprises at least one solenoid movably mounted near one end of the baseplate, so that actuating the solenoid produces an attractive force uponthe base plate and causes a resultant rotation of the base plate towardthe solenoid.
 4. The apparatus of claim 3 in which the means foractuating the solenoid comprises at least one optical switch movablymounted within the path of rotation of the attachment part and circuitmeans for controlling the interaction between the optical switch and thesolenoid so that traversal of the optical switch by the weighted partresults in the alternate actuation and deactuation of the solenoid.
 5. Amethod for determining the mechanical design properties of elasticmaterials comprising: supporting a sample at one end, attaching aweighted part to the other end of the sample, producing a periodictransient displacement of the supported end of the sample so as toinduce periodic motion of the sample, the magnitude of the displacementbeing of a predetermined value, and the period of the displacement beingdetermined by the period of the sample, so as to achieve a steady stateoscillation of the sample.
 6. The method of claim 5 in which thetransient displacement produced is angular, and its magnitude isdetermined by the relationship: theta o 2l/h Delta epsilon where l isthe length of the sample, h is the thickness of the sample, and Deltaepsilon is the desired maximum permanent deformation, and in which thedesign modulus is related to the steady state frequency of oscillationof the sample E 473.7 lJ/bh3 f2 wherein E is the design modulus, l isthe sample length, b is the sample width, h is the sample thickness, Jis the mass moment of inertia of the attachment part, and f is themeasured frequency of rotation of the part, and the design stress isrelated to the steady state amplitude of oscillation of the sampleaccording to: sigma 1 E ( epsilon 1 - Delta epsilon ) where sigma 1 isthe design stress, E is the design modulus, Delta epsilon is the offset,and epsilon 1 is the design strain which is a function of the steadystate amplitude of the angle of rotation according to the relationship:epsilon 1 0.00759 (h/l) phi a where phi a is the steady state or maximumamplitude.
 7. The method of claIm 5 in which the sample is a striphaving a length at least 12 times its thickness h and in which theoscillation comprises a uniform cyclic bending of the strip about a bendaxis transverse to the length of the strip.